Typodestroyer, arena decks lose hp based on how long they've been in the arena. The longer they're in, the more hp they lose. On the arena menu, if you hover over the question mark next to the "Age" stat, you can see how much this penalty is based on how old the deck is.
The hard badge is actually very easy. You just have to run in a circle to avoid the swordsman, kill the archers asap, and when there are no archers, kill only a few swordsman at a time so you can keep the archer population under control.
Note: Only shoot the boss once when he slams down to the ground. Your other shots won't have any effect on him. I was confused at first and kept running out of ammo.
It would be nice if there were an easier way to determine if you've already opened a treausre chest or not, like maybe having a big hole in the front of the chest or just having the chest dissapear altogether.
 "Elements"){kind=icon}
 "Dojo of Death"){kind=icon}
 "Johnny Upgrade"){kind=icon}
 "BoomsticK"){kind=icon}
 "The Legend of the Golden Robot"){kind=icon}
 "Icy Gifts"){kind=icon}
 "Epic Battle Fantasy 3"){kind=icon}
 "Demolition City"){kind=icon}
 "Sonny 2"){kind=icon}
 "Robot Dinosaurs That Shoot Beams When They Roar"){kind=icon}